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This work generalizes the fermion-like formulation of the Maxwell
theory to the non-Abelian Yang-Mills theory without matter fields.
This is a new representation of the Lie algebra valued electric
and magnetic fields. The resulting equations of motion are
invariant under the chiral transformation. In this formulation,
duality is a kind of chirality. We may also define local duality
transformations in terms of space-time dependent parameters. There
is an $N=1$ supersymmetry for the Dirac-like operator in this
representation.
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